Maxwell-Modified Metric Affine Gravity

TL;DR

This paper develops a gauge formulation of Maxwell-modified metric affine gravity, introducing new gauge fields that act as inflaton vectors and relate to dark energy, leading to Einstein-like equations with cosmological implications.

Contribution

It presents a novel gauge formulation extending special affine algebra with tensor generators, resulting in a Maxwell-modified gravity theory with potential cosmological applications.

Findings

Derives Einstein-like equations with additional gauge field sources.

Identifies shear curvature tensor with dark energy.

Proposes gauge fields as inflaton vectors driving accelerated expansion.

Abstract

We present a gauge formulation of the special affine algebra extended to include an antisymmetric tensorial generator belonging to the tensor representation of the special linear group. We then obtain a Maxwell modified metric affine gravity action with a cosmological constant term. We find the field equations of the theory and show that the theory reduces to an Einstein-like equation for metric affine gravity with the source added to the gravity equations with cosmological constant \mu contains linear contributions from the new gauge fields. The reduction of the Maxwell metric affine gravity to Riemann-Cartan one is discussed and the shear curvature tensor corresponding to the symmetric part of the special linear connection is identified with the dark energy. Furthermore, the new gauge fields interpreted as geometrical inflaton vector fields which drive accelerated expansion.